Test 2 Flashcards
Bateman Equation
Ad=Ap(0)(e^(kpt)-e^(kdt))kd/(kd-kp)
Where p = parent, d = daughter. Note also that Ad(0)e^(kdt) is activity of parent over time.
Definition of Reference Man
As originally defined in ICRP 23 (but later changed in ICRP 89): 70kg, 170cm, Caucasian, living in 10~20C, and 20~30 years old.
Snyder-Fisher Mathematical Model
Used for calculating dose in other organs due to source organ emitting radioactivity. A phantom was created to represent this model.
Exposure, Dose, Equivalent Dose, and Effective Dose calculation
Dose D = exposure X * constant
Equivalent dose H = Beam Quality Q (ICRP 26) * D
or Radiation Weighting Factor Wr (ICRP 60) * D
Effective dose E = sum (Tissue Weighting Factor * H) for all tissues involved
ICRP 30 (~1980)
Includes Part 2 and addendum on Part 4: “Limits for Intakes of Radionuclides by Workers.”
ICRP 26 (1977)
This publication of ICRP introduced quality factor for ionizing radiation, introduced dose equivalent, effective dose equivalent, and set up basic internal dosimetry concepts.
ICRP 26 Formulation of Internal Dosimetry
Source and target organs concept introduced. Absorbed fraction concept introduced (absorbed energy / emitted energy). Quality factors defined for beta, alpha, neutrons, and gamma. Tissue weighting factor defined. Equivalent dose for 50 years, H50 = sum (Quality factor * dose for 50 years), defined.
ALI (Annual Limit on Intake)
Activity of nuclide taken in that would itself alone result in EFFECTIVE DOSE (not equivalent!) of 50 mSv (annual dose limit). ***UNIT: Bq/yr
Stochastic Limit for ALI Calculation
Assume 50 mSv 50-year EFFECTIVE DOSE limit to calculate ALI in Bq/yr. We can do so by dividing 50 mSv by effective dose per decay!
Nonstochastic Limit for ALI Calculation
Assume 500 mSv 50-year EQUIVALENT DOSE (H50=Wr * D) limit to calculate ALI in Bq/yr. We can do so by dividing 500 mSv by equivalent dose per decay!
NOTE: LENS OF EYE is an exception! Assume 150 mSv limit!
Solving for H, Equivalent dose given for 50 years
H = k * U * SEE, where U = # of decays, SEE = specific effective energy (equivalent dose per transformation, Wt * D / Bq), and k = constant for energy conversion
Specific Effective Energy Calculation
SEE = sum over different radiation types (Quality Q * Radioactive Yield Y * Energy Emitted E * absorbed fraction AF(T<-S) / Mass of Tissue M).
Basically, equivalent dose per decay on target organ T. May result in MeV/g.
Convert to Sv: SEE (MeV/g) * (1.6*10^-10) = SEE (Sv)
Quality Factors for various radiation sources (ICRP 26)?
Beta, gamma = 1
Fast neutron, proton = 10
Alpha, fission fragments = 20
Absorbed Fraction AF for SEE Calculation
Can be reasonably determined: AF = 1 for beta, alpha for S<-S; if target is sufficiently far away, AF =0 since beta/alpha stops in less than 1 mm in tissue.
formula for effective half-life given biological clearance half-life Tb and physical decay rate Tr
Teff = Tr * Tb / (Tr + Tb)
Note: this looks like effective mass, doesn’t it?
Three Mile Island 1979
43,000 Curies Krypton but less (15 Curies) of Iodine-131 released. 2 mrem within 50 miles of TMI to 2 mil.
1 mCi = ? MBq
37 MBq
Chernobyl 1986
Over 100 rad to 200 workers; over 400 rad to 30 workers (all dead); average of 20 rem to within 200 miles of the reactor, population of 272,800.
I-131: 17 million curies
Cs-137: 2 million curies
Tritium Exit Signs
Originally 15 Curies, self-luminating exit sign. Sold in US, still circulating.
Solubility in Tissue of Common Isotopes
Tritium: 0.02 ; Xenon: 0.1
How do you calculate equivalent dose rate dH/dt for people immersed in radioactive gas? Give three equations, one for external radiation due to surrounding gas, one for absorbed gas in tissue, and one for lung from inhaled gas.
Dose derived from activity concentration, Bq/g = (Bq/cm^3) / (g/cm^3)
External radiation: dH/dt = g(e) * k * C/p * s, where k is ratio of stopping powers in air versus in tissue k~1, C/p is activity concentration in Bq/g, and s is equivalent dose rate Sv/hr of air per Bq/g
Absorbed gas in lung: dH/dt = g(a) * [delta * C/p] * s, where delta is solubility
Air in lung: dH/dt = g(L) * C / (M/V) * s, where p is replaced with mass of lung and volume of AIR in lung
Xenon-133
Specific gamma constant: 0.15 Rcm^2/mCihr
So exposure = gamma * activity / distance^2. Biological half life 2 min, physical half life 5.27 days.
What is Cumulated Activity for instantaneous uptake? What is the formula for it?
Activity integrated over infinite time (total disintegrations)
A = Ao * 1.44 * Teff
where Teff is effective half life.
Find integral dose from cumulated activity.
Integral dose (g*rad) = A (uCi*hr) * delta, where delta is conversion from cumulated activity A to energy (g*rad is a unit of energy). This equation only applies if we assume all energy is absorbed by source organ.
What is Cumulated Activity for non-instantaneous uptake? Formula?
A = Ao * 1.44 * Teff * (Tue/Tu),
where Tue = Tu*Tp/(Tu+Tp). Notice how as Tu -> 0 (instantaneous uptake), Tue/Tu -> 1.
What is formula for delta, disintegration-to-energy conversion factor? (Used to calculate gramrad from uCihr)
delta = 2.13 * Y * E (gramrad/uCihr),
where Y = emission ratio (100% or less), E = energy emitted in MeV
Specific absorbed fraction
Absorbed fraction of dose released from source to target PER gram of target organ. = AF / mass of target.
Reciprocity theorem
Specific absorbed fraction is equal for source organ and target organ even if the source and target are switched. That is, AF(S<-T) / mass of source.
Mean Dose per Cumulated Activity, S
S(T<-S) * delta / m_T ].
MIRD Stands for?
Medical Internal Radiation Dose